Floating and Sinking

How can we calculate density?

A solid shotput is a metallic sphere of radius $4.9 \mathrm{cm}$. Find the mass of the shotput, if its density is $7.8 \mathrm{g}/\mathrm{cm}³$.

A measuring cylinder is filled with $50 \mathrm{mL}$ of water. A solid with mass $16 \mathrm{kg}$ is then lowered into the cylinder. The water level rises to $58 \mathrm{mL}$. Determine the density of the solid.

If an iron object is immersed in water, it displaces $4 \mathrm{kg}$ of water. How much is the buoyant force acting on the iron object in newton?

Match column I with column II and select the correct option from the given codes.

A small metallic piece weighs $50 \mathrm{g}$ and its volume is $20 {\mathrm{cm}}^3$. It is immersed in water. Calculate the

(a) the density of the metallic piece and

(b) upthrust on the metallic piece.

What is the density of a substance of mass $100 \mathrm{g}$ and volume $10 {\mathrm{cm}}^3$ ?

The mass of sun is $2.0\times {10}^{30} \mathrm{kg}$ and its radius is $7.0\times {10}^8 \mathrm{m}$. Find its mass density?

The SI unit of upthrust is _____.

A piece of wood is held underwater. The upthrust on it will be _____ the weight of the wood.

An empty tin container with its mouth closed has an average density equal to that of a liquid. The container is taken $2 \mathrm{m}$ below the surface of that liquid and is left there. Then the container will _____.

The buoyancy depends on:

A jar is filled with two non-mixing liquids $1$ and $2$ having densities $d_1$ and $d_2$, respectively. A solid ball, made of a material of density $d_3$, is dropped in the jar. It comes to equilibrium in the position shown in the figure. Which of the following is true for $d_1$, $d_2$ and $d_3$?

A body (without air space) of mass $150 \mathrm{g}$ and volume $250 {\mathrm{cm}}^3$ is put in water. Will it float or sink.

Two metal pieces when immersed in liquid experience equal upthrust on them, then :

A metal sphere is dipped in water. If at $0 °\mathrm{C}$& $4 °\mathrm{C}$ the buoyancies in water are ${\beta }_1$ and ${\beta }_2$ respectively, then :

The weight of the wooden block is $W$. The apparent weight of the body on floating water is

A block of wood of length $20 \mathrm{cm}$ and area of cross-section $5 {\mathrm{cm}}^2$, floats in water with $\frac{2}{5}$ of its length above water.

Calculate: (i) Density of wood (ii) Weight of wood (iii) Extra force required to completely submerge it in water.

A cubical object of side $2 \mathrm{m}$ and density $200 \mathrm{kg}/{\mathrm{m}}^3$ is floating on water. Calculate the depth of the body in meters that is immersed in water. Take density of water as $1000 \mathrm{kg}/{\mathrm{m}}^3$.

An ice berg of density $900 \mathrm{kg} {\mathrm{m}}^{-3}$ is floating in water of density $1000 \mathrm{kg} {\mathrm{m}}^{-3}$. The percentage of volume of ice-cube outside the water is